It points to plans to create 500 free schools, the creation of new executive head roles in multi-academy trusts and the conversion of schools into academies.

“Our initial estimate is that this could result in over 1,000 additional vacancies over the next five years,” the report says.

But school governors say the quality of applications for some headship positions is “shocking”.

The trust believes better talent-spotting could be a solution. It also points out that negative perceptions of headship as a high-pressure role, and a possible career risk – for those trying to turn around challenging schools – are putting people off the job.

Heath Monk, CEO of the Future Leaders Trust, said: “Fewer people are applying to become heads and that means even fewer people are applying to lead schools that serve our most disadvantaged students. Without effective and inspiring leadership these children are losing out on the education they need.

“The talent is out there but many people need encouragement to understand they can step up. The solution is for existing heads to spot potential leaders in their schools and inspire them about headship.

“That means correcting the negative perceptions about the job and talking up its possibilities.

“We also need to know more about the problem. Our report draws on many different surveys but we don’t know how many schools are looking for a new head at any one time. We need the data to identify where the greatest demand is and know how many people are in the pipeline.”

Emma Knights, NGA chief executive, writes in the report that not enough is known about the causes of the shortage in school leaders.

“Headship can be pressured and potentially lonely, and maintaining a healthy work/life balance can be difficult,” she says.

“Although a good chair and governing board will support the head, this is the nature of top leadership posts. Is school leadership less attractive because of the data-driven accountability? Or could it be that teachers don’t seem to move around the country as much as other professionals?”

She also said that teachers’ lack of experience in applying for jobs could be a factor.

“Many governors have experience of recruiting in their professional lives, and the first time they are involved in school recruitment can be a surprise: the quality of some applications is shocking.”